[R] glmx specification of heteroskedasticity (and its use in Heckit)

[Michal Kvasnička]

Hallo.

Many thanks for your answer. Let me check please that I do understand
it correctly. Does it mean that the estimated log-likelyhood function
is (in the Gaussian case)

  sum y * log F(x'b / exp(z'g)) + sum (1 - y) * log(1 - F(x'b / exp(z'g))

where F is standard normal CDF, and the rest is as in your mail?

Many thanks once more.

Best wishes
Michal

P.S. Sorry if you get this mail twice -- I'm not yet certain with this
mailing list to what mail address I should reply.


2013/5/31 Achim Zeileis <Achim.Zeileis at uibk.ac.at>:
> On Fri, 31 May 2013, Michal Kvasni?ka wrote:
>
>> Hallo.
>>
>> First many thanks to its authors for glmx package and hetglm()
>> function especially. It is absolutely great.
>
>
> Glad it is useful for you!
>
>
>> Now, let me ask my question: what model of heteroskedasticity hetglm()
>> uses? Is the random part of the Gaussian probit model
>>
>>     norm(0,  sd = exp(X2*beta2))
>>
>> where norm is the Gaussian distribution, 0 is its zero mean, and sd is
>> its standard deviation modelled as a linear model with explanatory
>> variables X2 (a matrix) and some unknown parameters beta2?
>
>
> In the hetglm model the response y is distributed with mean mu and from some
> exponential family (default: binomial). And the following equation holds:
>
> mu = h( x'b / exp(z'g) )
>
> where h() is the inverse link function. Thus if h() is the normal
> distribution function (inverse probit link), then
>
> mu = P(X > 0)
>
> where X is normally distributed with mean x'b and standard deviation
> exp(z'g).
>
> Hope that helps,
> Z
>
>> I'm asking because after estimating a heteroskedastic probit, I want
>> to estimate a Heckit. I plan to use two-stage estimation procedure. In
>> the first step I want to estimate the heteroskedastic probit, and in
>> the second step the linear part (with bootstrapped confidence
>> intervals of parameters). The linear part includes inverse Mill's
>> ration lambda where
>>
>>    lambda = dnorm(X1*beta1, sd=?) / pnorm(X1*beta1, sd=?)
>>
>> where X1 are the explanatory variables of the probit model, and beta1
>> are their parameters. (I hope I can tweak the homoskedastic model this
>> way.) (I plan to use two-step estimation to avoid further distribution
>> assumptions on the linear part of the model.)
>>
>> Many thanks for your answer to my question (and also for any comment
>> on the overall estimation procedure).
>>
>> Best wishes,
>> Michal
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>